|About this Abstract
||2017 TMS Annual Meeting & Exhibition
||Computational Thermodynamics and Kinetics
||Nonlinear Elastic Effects in Phase Field Crystal and Amplitude Equations:Comparison to Ab Initio Simulations of bcc Metals and Graphene
||Claas Hüter, Martin Friak, Marc Weikamp, Jörg Neugebauer, Nigel Goldenfeld, Bob Svendsen, Robert Spatschek
|On-Site Speaker (Planned)
We advance the description of nonlinear elastic deformations in terms of the phase field crystal model and corresponding amplitude equation formulations. We identify the sources of geometric and constitutional nonlinearity. The former is expressed through a finite strain tensor based on the inverse right Cauchy-Green deformation tensor. It correctly catches the strain dependence of the stiffness for anisotropic and isotropic behavior, while the elastic energy can be expressed equivalently through the left deformation tensor only in isotropic one- and two-dimensional situations. In the isotropic low-temperature regime, the nonlinear elastic effects are related to the Birch-Murnaghan equation of state. The bcc amplitude equations yield a bulk modulus derivative K'= 4. If the strain dependence of the density wave amplitudes is taken into account, this reflects elastic weakening. For general anisotropic deformations, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.
||Planned: Supplemental Proceedings volume